An accurate and parallelizable geometric projector/backprojector for 3D PET image reconstruction

C code for an accurate projector/backprojector for Positron Emission Tomography (PET) image reconstruction has been developed. Iterative PET image reconstruction methods are supported by a projection/backprojection step built inside of any of such algorithms. It is not surprising that a more precise modeling of the forward process of the measurement will yield better results when solving the inverse problem of image reconstruction. Among the factors that can be include in this forward model are gamma-ray scatter contributions, attenuation, positron range, photon non-collinearity, crystal characteristics. Currently, we only include the geometric tube of response (TOR) modeling for a generic multi-ring scanner device. The elements in the transition matrix are calculated by a high statistics Monte Carlo simulation, taking advantage of the inherent symmetries and then the nonzero elements stored in a run length encoding incremental fashion. The resulting projector/backprojector is a voxel driven implementation. We show some preliminary results for 3D ML-EM reconstructions on synthetic phantom simulated data.